Advertisement

Robust Unsupervised and Semi-supervised Bounded ν − Support Vector Machines

  • Kun Zhao
  • Ying-jie Tian
  • Nai-yang Deng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5552)

Abstract

Support Vector Machines (SVMs) have been dominant learning techniques for more than ten years, and mostly applied to supervised learning problems. These years two-class unsupervised and semi-supervised classification algorithms based on Bounded C-SVMs, Bounded ν-SVMs, Lagrangian SVMs (LSVMs) and robust version to Bounded C − SVMs respectively, which are relaxed to Semi-definite Programming (SDP), get good classification results. But the parameter C in Bounded C-SVMs has no specific in quantification. Therefore we proposed robust version to unsupervised and semi-supervised classification algorithms based on Bounded ν− Support Vector Machines (Bν−SVMs). Numerical results confirm the robustness of proposed methods and show that our new algorithms based on robust version to Bν−SVM often obtain more accurate results than other algorithms.

Keywords

Bounded ν− support vector machines Semi-definite programming Unsupervised learning Semi-supervised learning Robust 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Sim, M.: Robust Optimization, Phd.Thesis MIT (2004)Google Scholar
  2. 2.
    Bertsimas, D., Sim, M.: The price of robustness. Opertions Research 52, 35–53 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Soyster, A.L.: Convex programming with set-inclusive constraints and applications to inexact linear programming. Oper. Res. 21, 1154–1157 (1973)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Ben-Tal, A., Nemirovski, A.: Rubust convex optimization. Math. Oper. Res. 23, 769–805 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Ben-Tal, A., Nemirovski, A.: Rubust solutions to uncertain programs. Oper. Res. Letters 25, 1–13 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Ben-Tal, A., Nemirovski, A.: Rubust solutions of linear programming problems constrained with uncertain data. Math. Program. 88, 411–424 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    El-Ghaoui, L., Lebret, H.: Rubust solutions to least-square problems to uncertain data matrices. SIAM J. Matrix Anal. Appl. 18, 1035–1064 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    El-Ghaoui, L., Oustry, F., Lebret, H.: Rubust solutions to semidefinite programs. SIAM J. Optim. 9, 33–52 (1998)CrossRefzbMATHGoogle Scholar
  9. 9.
    Schoelkopf, B., Smola, A.: Learning with kernels: Support Vector Machines, Regularization, Optimization, and Beyond. MIT Press, Cambridge (2002)Google Scholar
  10. 10.
    Lanckriet, G., Cristianini, N., Bartlett, P., Ghaoui, L., Jordan, M.: Learning the kernel matrix with semidefinite programming. Journal of Machine learning research 5 (2004)Google Scholar
  11. 11.
    De Bie, T., Crisrianini, N.: Convex methods for transduction. In: Advances in Neural Information Processing Systems (NIPS 2003), vol. 16 (2003)Google Scholar
  12. 12.
    Xu, L., Neufeld, J., Larson, B., Schuurmans, D.: Maximum margin clustering. In: Advances in Neural Information Processing Systems (NIPS 2004), vol. 17 (2004)Google Scholar
  13. 13.
    Kun, Z., Yingjie, T., Naiyang, D.: Unsupervised and Semi-Supervised Two-class Support Vector Machines. In: Proceedings of the Sixth IEEE International Conference on Data Mining Workshops, pp. 813–817 (2006)Google Scholar
  14. 14.
    Kun, Z., Yingjie, T., Naiyang, D.: Unsupervised and Semi-Supervised Lagrangian Support Vector Machines. In: Proceedings of the Seventh International Conference on Computational Science Workshops, pp. 882–889 (2007)Google Scholar
  15. 15.
    Kun, Z., Yingjie, T., Naiyang, D.: Robust Unsupervised and Semisupervised Bounded C − Support Vector Machines. In: Proceedings of the Seventh IEEE International Conference on Data Mining Workshops, pp. 331–336 (2007)Google Scholar
  16. 16.
    Friess, T., Christianini, C.N., Campbell, C.: The Kernel Adatron Algorithm: A Fast and Simple Learning Procedure for Support Vector Machines. In: Proceeding of 15th Intl. Con Machine Learning, Morgan Kaufman Publishers, San Francisco (1998)Google Scholar
  17. 17.
    Cristianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines and Other Kernel-based Learning Methods. Cambridge University Press, Cambridge (2000)CrossRefzbMATHGoogle Scholar
  18. 18.
    Jos, F.S.: Using SeDuMi1.02, A Matlab Toolbox for Optimization over Symmetric Cones. Optimization Methods and Software 11-12, 625–653 (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Kun Zhao
    • 1
  • Ying-jie Tian
    • 2
  • Nai-yang Deng
    • 3
  1. 1.Logistics SchoolBeijing Wuzi UniversityBeijingChina
  2. 2.Research Center on Fictitious Economy and Data ScienceChinese Academy of SciencesBeijingChina
  3. 3.College of ScienceChina Agricultural UniversityBeijingChina

Personalised recommendations